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Mathematics

1 answer:

Nitella [24]3 years ago

5 0

Answer:

50x⁴ - 20x² + 1 = 0

1. Quadratic form

50(x²)² - 20x² + 1 = 0

2. U is

x² = u

3. U- substitution

50u² - 20u + 1 = 0

4. Find the discriminant and identify roots

d = (-20)² - 4*1*50 = 200
u = (20 ± √200)/100
u = (2 ± √2)/10

Solve for x

x² = (2 ± √2)/10
x = ± √((2 ± √2)/10), four roots

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Given log4(3) =0.7925 and log4(5) =1.1610, use log properties to find log4(300).

Ede4ka [16]

Answer:

4.1145

Step-by-step explanation:

You can use the following formula to solve this kind of problems,

$log_{a}(b) + log_{a}(c) = log_{a}(bc)$

So, let's start of with log4_(300). Since the question have already gave log4_(3) =0.7925 and log4_(5) =1.1610. It means that you have to split the 300 into the simplest form where almost all of the numbers are 3 and 5.

$log_{4}(300) = log_{4}(4 \times 5 \times 3 \times 5) \\ = log_{4}(4) + log_{4}(5) + log_{4}(3) + log_{4}(5) \\ = 1 + 1.1610 + 0.7925 + 1.1610 \\ = 4.1145$